Chapter 5 - Polynomials and Factoring - 5.2 Factoring Trinomials of the Type x2+bx+c - 5.2 Exercise Set - Page 317: 14

$(y+1)(y+7)$

The 2 numbers whose product is $ac= 1(7)=7 $ and whose sum is $b= 8 $ are $\left\{ 1,7 \right\}.$ Using these two numbers to decompose the middle term of the given trinomial, $ y^2+8y+7 ,$ then \begin{array}{l}\require{cancel} y^2+1y+7y+7 \\\\= (y^2+y)+(7y+7) \\\\= y(y+1)+7(y+1) \\\\= (y+1)(y+7) .\end{array}